Tight binding models for ultracold atoms in honeycomb optical lattices

TL;DR

This paper develops detailed tight-binding models for ultracold atoms in honeycomb optical lattices using maximally localized Wannier functions, including up to third-nearest neighbors, and evaluates their accuracy against exact spectra.

Contribution

It introduces a systematic method to construct and analyze tight-binding models for honeycomb optical lattices with high accuracy using MLWFs.

Findings

Tight-binding models with up to third-nearest neighbors are feasible.

Explicit calculations of tunneling coefficients match experimental parameters.

Models accurately reproduce the Bloch spectrum within typical experimental conditions.

Abstract

We discuss how to construct tight-binding models for ultra cold atoms in honeycomb potentials, by means of the maximally localized Wannier functions (MLWFs) for composite bands introduced by Marzari and Vanderbilt [1]. In particular, we work out the model with up to third-nearest neighbors, and provide explicit calculations of the MLWFs and of the tunneling coefficients for the graphene-lyke potential with two degenerate minima per unit cell. Finally, we discuss the degree of accuracy in reproducing the exact Bloch spectrum of different tight-binding approximations, in a range of typical experimental parameters.